Bone angle in python
Test code that equates the angle between the two bones.  It doesn't take into account bone roll.

import bpy
from math import degrees

from bpy import context
arm = context.object

pb1 = arm.pose.bones.get("Bone")
pb2 = arm.pose.bones.get("Bone.001")

v1 = pb1.head - pb1.tail
v2 = pb2.head - pb2.tail

if pb1 and pb2:
    print(degrees(v1.angle(v2)))
else:
    print("Invalid bone name(s)")